Interpolation via translations
João Rasga, Walter Alexandre Carnielli, Cristina Sernadas · Mathematical logic quarterly · 2009
Abstract A new technique is presented for proving that a consequence system enjoys Craig interpolation or Maehara interpolation based on the fact that these properties hold in another consequence system. This technique is based on the existence of a back and forth translation satisfying some properties between the consequence systems. Some examples of translations satisfying those properties are described. Namely a translation between the global/local consequence systems induced by fragments of linear logic, a Kolmogorov‐Gentzen‐Gödel style translation, and a new translation between the global consequence systems induced by full Lambek calculus and linear logic, mixing features of a Kiriyama‐Ono style translation with features of a Kolmogorov‐Gentzen‐Gödel style translation. These translations establish a strong relationship between the logics involved and are used to obtain new results about whether Craig interpolation and Maehara interpolation hold in that logics (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)